prove sin(x)=1

Solution

prove

sin (x) = 1

False

Solution steps

sin (x) = 1

Show that the two sides are not equal

For

sin (x) = 1

plug in

x = 0

sin (0) = 0

sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0

The two sides are not equal

\Rightarrow False

sin (θ) tan (θ) = \frac{1 - cos ^{2} ( θ )}{cos ( θ )}

sin (x + 3 0^{\circ}) + 3 cos (x + 3 0^{\circ}) = 2 cos (x)

(sec (a) + tan (a)) (1 - sin (a)) = cos (a)

tan^{2} (a) + 1 = sec^{2} (a)

\frac{8 csc ( - x )}{sec ( - x )} = - 8 cot (x)